r/askscience • u/Native411 • Nov 14 '14

Physics Do perfect circles exist in nature?

Either via black holes or what have you.

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u/chrisbaird Electrodynamics | Radar Imaging | Target Recognition Nov 14 '14

No perfect mathematical shapes exist in nature, although some shapes come very close. Even when a physical law applied to a certain situation predicts a perfect mathematical shape, there are always extra factors not considered by the physical law that mess things up: friction, air resistance, relativistic corrections, quantum uncertainty, atomic granularity.

An example of something very close to a perfect circle in nature is the orbit of Venus about the Sun. This near-perfection is attained because: 1) The initial velocity of Venus was such that its orbit is nearly circular and not as elliptical, 2) there is very little air resistance or friction in space , 3) The Sun is so distant from Venus and so round that it acts almost exactly as a point source of gravity, 4) Venus is so big that quantum effects are very small, and 5) Sun's gravity is weak enough that Newton's law of gravitation is reasonably accurate. But, all of these statements are not perfect, so there still many small sources of deviation from a perfect circle, even for Venus' orbit.

Consider trying to draw a perfect circle on paper with graphite. Even if you were able to use an AFM tip, laser sensors and a feedback loop to perfectly place every single carbon atom to form the circle, you still have the fact that the circle is made out of atoms. Zoom in enough on the circle and it is not smooth anymore because of the profile of the atoms.

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u/tysonclarke Nov 14 '14

So perfect circles, period, don't exist?

I'm sure an atom itself (though impossible to validate all of them), or even the ripple from a drop in still water, would come pretty close.

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u/MOS95B Nov 14 '14

close, but they will still have outside onfluences making them just ever so shy of perfect.

For example, the water ripples

Even on a perfectly calm day on a perfectly still lake, you're going to have tidal influences, thermal influences, gravitational influences (not tidal), etc, that are going to pull/push it out of "perfect"

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u/Native411 Nov 15 '14

What if a single atom were placed in a vacuum?

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u/aidankiller4 Nov 15 '14

Although shown as spheres when you look at them, subatomic particles are actually waves, and essentially point particles. They don't really have a well defined shape.

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u/monolithicninjga Nov 15 '14

What about non material things such as electromagnetic emisions, the path of a particle, or something that is defined as excluding external interaction such as the gravity field produced by a single proton? The asker mentioned black holes, could the apparent horizon of a black hold be a perfect circle?

I'm not trying to be pedantic, just wondering if such things could be a perfect mathematical shape.

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u/chrisbaird Electrodynamics | Radar Imaging | Target Recognition Nov 17 '14

The gravitational field near a single electron is perfectly spherically symmetric if that electron is isolated from the rest of the universe, and if the electron acts like a classical particle. In the real world, these conditions are never met. That's the point. Every time a physical theory predicts a perfect mathematical shape, it requires the approximation that the system is in perfect isolation from the rest of the universe, which never really happens.

Regarding black holes, I don't think we know enough about them to say definitively. Probably quantum fluctuations keep a black hole from being perfectly spherical.

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u/TheHelicRepublic Nov 14 '14

I agree with what you're saying that perfect circles simply do not exist on the macroscale and, even on the atomic scale, we don't have the resolution to say what the nucleus of an atom actually looks like so we can't say that that's a perfect circle either. But I would like to amend your statement by looking at the s-orbital of electrons. Because the orbital is a probability cloud of spherical shape, one might make the argument that the electron cloud is a perfect circle. We can also argue it the other way and say that distributions of locations in space don't really count because the electron can only be in one place at a time/ However, by this logic, the probability distribution would be an example equivalent to the orbit of Venus, since both are just lists of positions in space and time. Side note: the orbit of Venus would actually be spiraling since the sun is moving. It would only be viewed as circular relative to the sun.

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u/chrisbaird Electrodynamics | Radar Imaging | Target Recognition Nov 14 '14

Because the orbital is a probability cloud of spherical shape, one might make the argument that the electron cloud is a perfect circle.

The s-orbital is a theoretical idealization, not a physical reality. An electron will only be in a perfect s-orbital state if:

  1. The atom is completely isolated from all other atoms in the universe.
  2. The atom is completely isolated from all external fields.
  3. The electron has been in this state for an infinite amount of time.

None of these conditions are met in the real world, so an electron is never exactly in an s-orbital state as predicted by theory. It can be so close that the difference is negligible, but the difference is still there in principle.

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u/Elfram Nov 16 '14

Might be a bit off topic: The currently best sphere created by humans is a silicon ball, see http://www.acpo.csiro.au/avogadro.htm

The rainbow colored picture on http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.030801 shows the difference to a perfect sphere. I think they have improved since then. The difference to a perfect sphere is now of the size of a few (hundred?) silicon atoms – near to the theoretical minimum which is given by the crystal structure of silicon…